| 唐丹,王永进,张冠男.分式噪声驱动的一类随机偏微分方程的非参数估计}[J].数学年刊A辑,2013,34(5):627~642 |
| 分式噪声驱动的一类随机偏微分方程的非参数估计} |
| Nonparametric Inference for a Class of SPDEs Driven by Fractional Noises |
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| DOI： |
| 中文关键词: 分式噪声, 非参数统计, 随机偏微分方程 |
| 英文关键词:Fractional noise, Nonparametric inference, Stochastic partial
differential equation |
| 基金项目:国家自然科学基金 (No.11101083)和对外经济贸易大学学术创新团队资助项目(数量经济学理论与应用创新团队)(No.CXTD4-01) |
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| 中文摘要: |
| 研究了一类由分式噪声所驱动的随机偏微分方程的统计推断. 先构造了偏微分算子时间
相依系数的非参数估计量, 然后得到了该估计在最大值范数下的收敛率和渐近正态性. 该收敛率
由系数的平滑参数和分式噪声的Hurst参数共同决定. |
| 英文摘要: |
| The nonparametric inference for a class of stochastic partial differential equations
driven by fractional noises is investigated. The authors construct a non-parametric estimator
of the time-dependent coefficient of the partial differential operator. The convergence in the
sup-norm and asymptotic normality of the estimator are established. The rate of convergence
is determined by both the smoothness of the coefficient and the Hurst parameter of the
fractional noise. |
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